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This chapter begins with the difference between independent and dependent variables. It then describes three types of research designs. It introduces six ways to collect data on students. These include a review of records, teacher interviews, daily or weekly logs, standardized instruments, direct observation, and scaled questions. The frequency of data collection is identified as dependent on three primary factors: the type of research design, the instrument used, and the intensity of intervention. The chapter also introduces using an Excel spreadsheet to record and analyze the data that is collected. This includes some instructions on data entry, descriptive statistics, and inferential statistics. The chapter concludes with two important cautions. First, there is a difference between correlation and causation. Second, there is a difference between clinical significance and statistical significance.

This chapter includes several new sections on inferential analysis of public health surveillance data. It provides a guide using a thoughtful approach to complex statistical analyses for the data rich environment in which surveillance practitioners find themselves. Included in this chapter are sections on trend analyses, survival (or time-to-event) analyses, analyses of associations in cross sectional data, analyses of data from complex survey designs, aberration detection analysis, detection of clustering, and mapping and geo-analyses. New examples from actual public health surveillance systems are used to demonstrate analytic techniques.

This chapter explores the statistical pattern of the galaxy distribution. It focuses on n-point correlation functions (analogs of the autocorrelation function and higher moments for a continuous function), the descriptive statistics that have proved useful. The approach has also proved useful in many other applications. Of considerable practical importance has been the fact that there is a simple linear equation relating the directly observable angular correlation function to the wanted spatial function. This means the translation from one to the other is fairly easy, and equally important it makes it easy to say how the statistical estimates ought to scale with the depth of the survey and hence to test for possible contamination of the estimates by systematic errors. A third useful result is that the dynamics of the galaxy distribution can be treated in terms of the mass correlation functions: the statistic that proves useful for the reduction of the data may also be useful for the analysis of the theory.

This first chapter provides an overview of the steps for completing a research project, offers a one-paragraph introduction to R, shows how to install R and its add-on packages, mentions how to get help, presents an example of how to write and execute a simple R program as an ice-breaker, demonstrates how to create, describe, and graph a variable in R with a simple numerical example, illustrates how to report descriptive statistics in a table, and concludes by applying the R code to a real-world data example from a published article. The chapter also shows common coding errors and a variety of logical and mathematical operators, how to use R on Mac machines, how to export output from R, and how to install and use RStudio.

This chapter covers the final three steps of the nine-step process for conducting mixed methods research in social work. It begins by describing how to prepare qualitative and quantitative data for analysis, then provides some helpful techniques for efficiently coding and analyzing qualitative data. A basic description of how to analyze quantitative data is provided, as well as how it can be used to provide descriptive statistics (such as crosstabs, frequencies, and distributions), measures of central tendency, measures of variability, and measures of association. The chapter also briefly discusses how to maximize rigor and the relevance of analysis procedures for analyzing qualitative and quantitative data. The chapter concludes with some useful tips on the actual “mixing” of mixed methods research, the various points in time during which mixing can occur, and the ways data can be integrated and interpreted.

This chapter introduces the basics of statistics and probability theory that will be used throughout the book. Specifically, it introduces the concepts behind descriptive statistics, including aspects of using visualization of means, medians, and modes, as well as distribution visualizations to understand your data for further analysis. It also introduces inferential statistics, specifically discussing t-tests and ANOVA, discussing the assumptions used for each of the tests and outputs. The chapter also includes labs where we use real game data to give you a practical understanding of how to apply these concepts and tests and how to interpret the meaning of the results you get from each test and method.

Chapter 2 provides a review of descriptive statistical methods commonly used in social science research. First, the authors consider the steps involved in defining the variables used in a study, and determining how they will be measured. The four possible levels at which variables can be measured (i.e., nominal, ordinal, interval, and ratio) are reviewed. Next, frequency and percentage distributions, and other graphical representations of data are presented. The most commonly used measures of central tendency—the mode, median, and mean—and the most commonly used measures of variability—the range, variance, and standard deviation—are described. Finally, detailed directions on how to calculate each of these statistics are offered using mathematical formulas and the statistical computer package, SPSS.

Descriptive statistics allow researchers to use numbers to begin to tell the stories that exist in their data. This chapter presents an overview of the basic statistical tools researchers can use to summarize, display, and interpret data. The chapter presents guidelines for interpreting data and examples of typical sorts of data that music education researchers may gather. Statistical analyses suitable for identifying how data are distributed, determining typical values of a distribution, and describing how individuals differ on measured variables of interest are described. Approaches for graphing data that are appropriate for variables of different measurement scales are also described.

Chapter 10 of Performing Music Research sets out the fundamental principles that underpin all statistics. Statistics must be used with care, and strict conditions govern their deployment, many of which have to be considered in the earliest stages of research. The chapter discusses techniques for organizing, describing, and summarizing data. It introduces the concepts of central tendency and variability, as it is essential for carrying out statistical tests to know the difference between means, medians, and modes, and when and how to use them, and to understand how data vary within, as well as between, samples.

All hurricanes are different. Statistics helps you characterize hurricanes from the typical to the extreme. In this chapter, we provide an introduction to classical (or frequentist) statistics. To get the most out of it, we again encourage you to open an R session and type in the code as you read along. Descriptive statistics are used to summarize your data. The mean and the variance are good examples. So is correlation. Data can be a set of weather records or output from a global climate model. Descriptive statistics provide answers to questions like does Jamaica experience more hurricanes than Puerto Rico? In Chapter 2, you learned some functions for summarizing your data, let us review. Recall that the data set H.txt is a list of hurricane counts by year making landfall in the United States (excluding Hawaii). To input the data and save them as a data object, type . . . > H = read. Table ("H.txt", header=TRUE) . . . Make sure the data file is located in your working directory. To check your working directory, type getwd (). Sometimes all you need are a few summary statistics from your data. You can obtain the mean and variance by typing . . . > mean (H$All); var (H$All) [1] 1.69375 [1] 2.10059 . . . Recall that the semicolon acts as a return so you can place multiple functions on the same text line. The sample mean is a measure of the central tendency and the sample variance is a measure of the spread. These are called the first-and second-moment statistics. Like all statistics, they are random variables. A random variable can be thought of as a quantity whose value is not fixed; it changes depending on the values in your sample. If you consider the number of hurricanes over a different sample of years, the sample mean will almost certainly be different. Same with the variance. The sample mean provides an estimate of the population mean (the mean over all past and future years).

This chapter presents the modeling results and their interpretation. First, the synthesis of success factors from existing success factor syntheses is developed and theoretically motivated. Then, the descriptive statistics and correlations between success factors are described analogously for each data set (CPR, NIIS, IFRI, and an overall model from all data sets). Finally, for each modelling methodology (multivariate regressions, random forests, and neural network), the model qualities are presented. In addition, the individual factors are described according to their importance for ecological success. Each presentation of results is followed by a discussion. The chapter is concluded with robustness and sensitivity analyses.

The chapter presents descriptive statistics about two patient groups. The areas shown are: family background, labour-market attainment, criminal history, traffic accidents, childhood outcomes, family situation, and general health care. The statistics show that (i) parents of individuals with ADHD are younger and earn less than parents of the average person in the rest of the population; (ii) individuals who have ADHD on average have less education, are more likely to be out of the labour force, and earn significantly less than members of the general population; (iii) persons with ADHD are more likely to engage in criminal activity and, when they do, these crimes are more serious than crimes committed by other individuals; (iv) individuals with ADHD use both the primary and the secondary health-care sector more than average, and their medicine costs are higher than average.

This chapter contains supplementary information on all parts of the book. It includes the description how variables have been recoded, and the expert evaluation results on the relevance of the success factors for ecological success. Furthermore, all variables for ecological success are described for each data set (CPR, NIIS, IFRI). These tables are followed by the descriptive statistics, histograms and full correlation matrices of the success factors. Next, the comprehensive success factor synthesis consisting of 260 variables is presented. The chapter concludes with the reference section.

This book is about hurricanes, climate, and statistics. These topics may not seem related. Hurricanes are violent winds and flooding rains, climate is about weather conditions from the past, and statistics is about numbers. But what if you wanted to estimate the probability of winds exceeding 60 ms−1 in Florida next year. The answer involves all three, hurricanes (fastest winds), climate (weather of the past), and statistics (probability). This book teaches you how to answer these questions in a rigorous and scientific way. We begin here with a short description of the topics and a few notes on what this book is about. A hurricane is an area of low air pressure over the warm tropical ocean. The low pressure creates showers and thunderstorms that start the winds rotating. The rotation helps to develop new thunderstorms. A tropical storm forms when the rotating winds exceed 17 ms−1 and a hurricane when they exceed 33 ms−1. Once formed, the winds continue to blow despite friction by an in-up-and-out circulation that imports heat at high temperature from the ocean and exports heat at lower temperature in the upper troposphere (near 16 km), which is similar to the way a steam engine converts thermal energy to mechanical motion. In short, a hurricane is powered by moisture and heat. Strong winds are a hurricane’s defining characteristic. Wind is caused by the change in air pressure between two locations. In the center of a hurricane, the air pressure, which is the weight of a column of air from the surface to the top of the atmosphere, is quite low compared with the air pressure outside the hurricane. This difference causes the air to move from the outside inward toward the center. By a combination of friction as the air rubs on the ocean below and the spin of the earth as it rotates on its axis, the air does not move directly inward but rather spirals in a counter clockwise direction toward the region of lowest pressure.

After preparing your dataset, the business problem should be quite familiar, along with the subject matter and the content of the dataset. This section is about modeling data, using data to train algorithms to create models that can be used to predict future events or understand past events. The section shows where data modeling fits in the overall machine learning pipeline. Traditionally, we store real-world data in one or more databases or files. This data is extracted, and features and a target (T) are created and submitted to the “Model Data” stage (the topic of this section). Following the completion of this stage, the model produced is examined (Section V) and placed into production. With the model in the production system, present data generated from the real-world environment is inputted into the system. In the example case of a diabetes patient, we enter a new patient’s information electronic health record into the system, and a database lookup retrieves additional data for feature creation.

This chapter presents a summary of the entire book. It is written for readers who may not have time for more intensive reading, such as policy makers. The chapter gives a presentation of the characteristics of ADHD, describes how adults with ADHD are identified from Danish register data, presents descriptive statistics for adults with ADHD compared to the general adult population in Denmark, presents calculations of private and social costs of ADHD broken down into private and public costs, discusses generalizability of the established results beyond Denmark, and presents recommendations that might mitigate the early impact of ADHD on academic attainment, family well-being, and early career productivity from an ‘invest-to-save’ perspective.

This chapter presents systematic descriptive evidence on the status of popular conceptions of democracy in today’s world, using GBS II data from seventy-one societies. To make the descriptive analysis more informative, we have included comparable information from the United States and relied on different psychometric models to uncover people’s latent characteristics that shape their responses to the PUD instruments. We have consistently found that the PUD instruments are sufficiently sensitive to the socioeconomic and political environment, thus revealing significant and substantial variation in popular conceptions of democracies across regions, between societies, and among individuals. To ensure that the variation documented in the PUD instruments is not something transient or idiosyncratic, we further explore the longitudinal dynamics of this critical attitude using the ABS two-wave rolling-cross-sectional surveys from thirteen East Asian societies.

Data analysis is not just about physically performing the analyses. We also need to think carefully about our data, and various issues that they might have. In this chapter, we explore conceptual issues raised by the bat diet workflow demonstration. This chapter discusses statistical variables, populations and samples, independence and non-independence in data, and working with numeric and categorical variables. In the last two items of that list, we look both at quantitative summaries of variables and relationships and also at graphical summaries.